The Mathematical Institute, University of Oxford, Eprints Archive

Binocular rivalry in a competitive neural network with synaptic depression

Kilpatrick, Z. P. and Bressloff, P. C. (2010) Binocular rivalry in a competitive neural network with synaptic depression. SIAM Applied Dynamical Systems . (Submitted)

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Abstract

We study binocular rivalry in a competitive neural network with synaptic depression. In particular, we consider two coupled hypercolums within primary visual cortex (V1), representing orientation selective cells responding either to left or right eye inputs. Coupling between hyper-
columns is dominated by inhibition, especially for neurons with dissimilar orientation preferences. Within hypercolumns, recurrent connectivity is excitatory for similar orientations and inhibitory for different orientations. All synaptic connections are modifiable by local synaptic depression. When the hypercolumns are driven by orthogonal oriented stimuli, it is possible to induce oscillations that are representative of binocular rivalry. We first analyze the occurrence of oscillations in a space-clamped version of the model using a fast-slow analysis, taking advantage of the fact that depression evolves much slower than population activity. We then analyze the onset of oscillations in the full spatially extended system by carrying out a piecewise smooth stability analysis of single (winner-take-all) and double (fusion) bumps within the network. Although our stability analysis only takes into account instabilities associated with real eigenvalues, it identifies points of instability that are consistent with what is found numerically. In particular, we show that in regions of parameter space where double bumps are unstable and no single bumps exist, binocular rivalry can arise as a slow alternation between either population supporting a bump.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1014
Deposited By:Peter Hudston
Deposited On:28 Oct 2010 14:34
Last Modified:09 Feb 2012 15:53

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